Did the random assignment work A large clinical trial of the

Did the random assignment work? A large clinical trial of the effect of diet on breast cancer assigned women at random to either a normal diet or a low-fat diet. To check that the random assignment did produce comparable groups, we can compare the two groups at the start of the study. Asked if there is a family history of breast cancer,3396 of the 19,541 women in the low-fat group and 4929 of the 29,294 women in the control group said “yes.”²⁶ If the random assignment worked well, there should not be a significant difference in the proportions with a family history of breast cancer. How significant is the observed difference? (4 step)

Solution

Null Hypothesis, There Is No Significance between them Ho: p1 = p2
Alternate Hypothesis, There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =3396, n1 =19541, P1= X1/n1=0.174
Sample 2 : X2 =4929, n2 =29294, P2= X2/n2=0.168
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.17
Q^ Value For Proportion= 1-P^=0.83
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.174-0.168)/Sqrt((0.17*0.83(1/19541+1/29294))
Zo =1.592
| Zo | =1.592
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =1.592 & | Z | =1.96
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 1.5918 ) = 0.1114
Hence Value of P0.05 < 0.1114,Here We Do not Reject Ho

We don\'t have evidence to indicate that there should n\'t be a significant difference in the proportions with a family history of breast cancer